Spectrum analysis is performed on many types of digital signals in a variety of applications. A Fast Fourier Transform (FFT) is typically used in such spectrum analysis to convert a time-domain digital signal to a frequency-domain signal. Nevertheless, the FFT by itself is generally inadequate to perform spectrum analysis because of artifacts introduced by the finite length of the digital-signal data record.
Those artifacts are controlled by "windowing" the signal. In the time-domain, windowing is performed by multiplying each input sample by a suitable time-domain weighting coefficient. This is illustrated by the assembly shown in FIG. 1, in which a multiplier 11 is connected to each (time-domain) input line 13 to the FFT 15. In the frequency-domain, the windowing is performed by convolving the FFT outputs with suitable frequency-domain weighting coefficients. The frequency-domain weighting coefficients are the Fourier transform samples of the time-domain weighting coefficients. FIG. 2 shows an FFT assembly with convolvers 21 on the (frequency-domain) output lines 23 of the FFT 25.
Generally, the choice of whether to window in the frequency-domain or in the time-domain is driven by both applications and mechanization considerations. In many applications, the input-data signal is too fast to permit time-domain windowing. However, because of the extremely large number of computations required for frequency-domain windowing, that method has also proved inadequate for extremely high-speed-data inputs. Additionally, the large processors required for the frequency-domain windowing has further limited the applications in which such windowing can be practically carried out.